Tauberian theorems for Abel limitability method

İbrahim Çanak; Ümit Totur

Open Mathematics (2008)

  • Volume: 6, Issue: 2, page 301-306
  • ISSN: 2391-5455

Abstract

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This paper addresses conditions for the Abel method of limitability to imply convergence and subsequential convergence.

How to cite

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İbrahim Çanak, and Ümit Totur. "Tauberian theorems for Abel limitability method." Open Mathematics 6.2 (2008): 301-306. <http://eudml.org/doc/269023>.

@article{İbrahimÇanak2008,
abstract = {This paper addresses conditions for the Abel method of limitability to imply convergence and subsequential convergence.},
author = {İbrahim Çanak, Ümit Totur},
journal = {Open Mathematics},
keywords = {Abel method of limitability; general control modulo; Tauberian conditions; slow oscillation; moderate oscillation; subsequential convergence; Abel summability},
language = {eng},
number = {2},
pages = {301-306},
title = {Tauberian theorems for Abel limitability method},
url = {http://eudml.org/doc/269023},
volume = {6},
year = {2008},
}

TY - JOUR
AU - İbrahim Çanak
AU - Ümit Totur
TI - Tauberian theorems for Abel limitability method
JO - Open Mathematics
PY - 2008
VL - 6
IS - 2
SP - 301
EP - 306
AB - This paper addresses conditions for the Abel method of limitability to imply convergence and subsequential convergence.
LA - eng
KW - Abel method of limitability; general control modulo; Tauberian conditions; slow oscillation; moderate oscillation; subsequential convergence; Abel summability
UR - http://eudml.org/doc/269023
ER -

References

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  1. [1] Çanak İ., Totur Ü., A Tauberian theorem with a generalized one-sided condition, Abstr. Appl. Anal., 2007, 60360 Zbl1155.40304
  2. [2] Dik F., Tauberian theorems for convergence and subsequential convergence of sequences with controlled oscillatory behavior, Math. Morav., 2001, 5, 19–56 Zbl1047.40005
  3. [3] Dik M., Tauberian theorems for sequences with moderately oscillatory control moduli, Math. Morav., 2001, 5, 57–94 Zbl1046.40004
  4. [4] Littlewood J.E., The converse of Abel’s theorem on power series, Proc. London Math. Soc., 1910, 9, 434–448 http://dx.doi.org/10.1112/plms/s2-9.1.434 Zbl42.0276.01
  5. [5] Rényi A., On a Tauberian theorem of O. Szász, Acta Univ. Szeged Sect. Sci. Math., 1946, 11, 119–123 Zbl0060.15703
  6. [6] Schmidt R., Über divergente folgen und lineare mittelbildungen, Math. Z., 1925, 22, 89–152 http://dx.doi.org/10.1007/BF01479600 Zbl51.0182.04
  7. [7] Stanojević Č.V., Analysis of Divergence: Control and Management of Divergent Process, Graduate Research Seminar Lecture Notes (Edited by İ. Çanak), University of Missouri-Rolla, 1998 
  8. [8] Stanojević Č.V., Analysis of Divergence: Applications to the Tauberian Theory, Graduate Research Seminar, University of Missouri - Rolla, 1999 
  9. [9] Stanojević Č.V., Stanojević V.B., Tauberian retrieval theory, Publ. Inst. Math., 2002, 71, 105–111 http://dx.doi.org/10.2298/PIM0271105S Zbl1027.40005
  10. [10] Tauber A., Ein Satz aus der Theorie der unendlichen Reihen, Monatsh. Math. Phys., 1897, 8, 273–277 http://dx.doi.org/10.1007/BF01696278 

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